Abstract

A Distributional (Single) Index Model (DIM) is a semiparametric model for distributional regression, that is, estimation of conditional distributions given covariates. The method is a combination of classical single-index models for the estimation of the conditional mean of a response given covariates, and isotonic distributional regression. The model for the index is parametric, whereas the conditional distributions are estimated nonparametrically under a stochastic ordering constraint. We show consistency of our estimators and apply them to a highly challenging dataset on the length of stay (LoS) of patients in intensive care units. We use the model to provide skillful and calibrated probabilistic predictions for the LoS of individual patients, which outperform the available methods in the literature.

摘要

分布（单）指数模型（DIM）是分布回归的半参数模型，即给定协变量的条件分布估计。该方法结合了经典的单指数模型，用于估计给定协变量的响应的条件均值和等渗分布回归。该指数的模型是参数化的，而条件分布是在随机排序约束下非参数化地估计的。我们展示了我们的估计量的一致性，并将它们应用于关于重症监护病房患者住院时间 (LoS) 的极具挑战性的数据集。我们使用该模型为个体患者的 LoS 提供熟练和校准的概率预测，其性能优于文献中的可用方法。